Question: Simplify; express your answer in exponential form. Assume $t\neq 0, a\neq 0$. $\dfrac{{t^{-4}a^{-3}}}{{(t^{4}a^{-1})^{-5}}}$
Explanation: To start, try simplifying the numerator and the denominator independently. In the numerator, we can use the distributive property of exponents. ${t^{-4}a^{-3} = t^{-4}a^{-3}}$ On the left, we have ${t^{-4}}$ to the exponent ${1}$ . Now ${-4 \times 1 = -4}$ , so ${t^{-4} = t^{-4}}$ Apply the ideas above to simplify the equation. $\dfrac{{t^{-4}a^{-3}}}{{(t^{4}a^{-1})^{-5}}} = \dfrac{{t^{-4}a^{-3}}}{{t^{-20}a^{5}}}$ Break up the equation by variable and simplify. $\dfrac{{t^{-4}a^{-3}}}{{t^{-20}a^{5}}} = \dfrac{{t^{-4}}}{{t^{-20}}} \cdot \dfrac{{a^{-3}}}{{a^{5}}} = t^{{-4} - {(-20)}} \cdot a^{{-3} - {5}} = t^{16}a^{-8}$